JAM

As far as I know, there is no part time IIT JAM. You will have to devote yourself to the exam if you want to secure a passing grade in the exam and qualify for M.Tech or M.Sc.
JAM 2018 eligibility criteria:
The common criteria across institutes for each programme are:
JAM eligibility criteria is common for each program across institutes for appearing in the postgraduate science admission test.
The candidates should have secured at least 55% in subjects including languages and subsidiaries of all the years combined. Those, however, belonging to SC/ST and OBC categories need to secure at least 50 percent marks in the subjects.
Candidates need to note that equivalence of marks in case of grades in letter/CGPA (and not in percentage of marks) will be decided by the participating institutes of JAM.
As per the JAM eligibility criteria 2018, candidates will need to submit their proof of qualifying degree examinations by September 30th, 2018 to the admitting institute. However, upon failing to do so will lead to cancellation of their candidature.

Some of the best books you can purchase to prepare for M.Sc. (JAM) are as follows:
1) Solved Papers & Practice Sets IIT JAM (Joint Admission Test for M. Sc. From IITs) - Mathematics by Neha Tyagi (Author)
2) A Complete Resource Manual M.Sc Mathematics Entrance examination by rashmi Gupta Suraj Singh (Author)
3) JAM Chemistry (for IIT JAM) (English, Shyam Narayan Aggarwal, Avijit Mukherjee)
4) Jam Physics For IIT Jam (English, Vishal Deoarshi, Jyoti Ahuja)
Best colleges which you can get if you qualify for the merit list through JAM are as follows:
https://www.shiksha.com/science/articles/colleges-accepting-iit-jam-scores-ranks-for-admission-blogId-13971